This paper aims to test the international transmission of stock market volatility and the risk of contagion among a sample of emerging and developed markets through a methodology rarely used in this context. This methodology, developed by Bai and Perron (1998, 2003), is based on the determination of structural breakpoints. Our empirical strategy consists in identifying similarities in the dates of structural breaks and in comparing them with the occurrence dates of financial crises in order to test respectively the international transmission of volatility and the risk of contagion. Empirical results lead to very interesting conclusions. First, we find that the transmission of volatility is effective between the emerging markets and between them and the developed ones. Second, we show that the geographical proximity has a crucial effect in the transmission of volatility. Finally, a comparison between the occurrence dates of financial crises and the different structural breakpoint dates allows us to notice that there is an important analogy between them. This proves that the financial shocks are transmitted from one market to another during the periods of crises.